Title: Inertial waves and modes excited by the libration of a rotating cube Show Chinese title

Title: 惯性波和由旋转立方体的摆动激发的模态

Abstract: We report experimental measurements of the flow in a cubic container submitted to a longitudinal libration, i.e. a rotation modulated in time. Velocity fields in a vertical and a horizontal plane are measured in the librating frame using a corotating particle image velocimetry system. When the libration frequency $\sigma_0$ is smaller than twice the mean rotation rate $\Omega_0$, inertial waves can propagate in the interior of the fluid. At arbitrary excitation frequencies $\sigma_0<2\Omega_0$, the oscillating flow shows two contributions: (i) a basic flow induced by the libration motion, and (ii) inertial wave beams propagating obliquely upward and downward from the horizontal edges of the cube. In addition to these two contributions, inertial modes may also be excited at some specific resonant frequencies. We characterize in particular the resonance of the mode of lowest order compatible with the symmetries of the forcing, noted [2,1,+]. By comparing the measured flow fields to the expected inviscid inertial modes computed numerically [L.R.M. Maas, Fluid Dyn. Res. \textbf{33}, 373 (2003)], we show that only a subset of inertial modes, matching the symmetries of the forcing, can be excited by the libration. Show Chinese abstract

Abstract: 我们报告了在纵向摆动作用下的立方容器中的流动实验测量，即时间调制的旋转。使用随转粒子图像测速系统，在摆动参考系中测量了垂直和平面内的速度场。当摆动频率$\sigma_0$小于平均旋转速率$\Omega_0$的两倍时，惯性波可以在流体内部传播。在任意激励频率$\sigma_0<2\Omega_0$下，振荡流动显示两个贡献：(i) 由摆动运动引起的基底流动，以及 (ii) 从立方体水平边沿斜向上和向下传播的惯性波束。除了这两个贡献外，某些特定的共振频率下也可能激发惯性模态。我们特别研究了与激励对称性相容的最低阶模态的共振，记为 [2,1,+]。通过将测量的流动场与数值计算的无粘惯性模态进行比较 [L.R.M. Maas, Fluid Dyn. Res.\textbf{33}, 373 (2003)]，我们表明只有与激励对称性匹配的一小部分惯性模态可以通过摆动激发。